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2. inverse trigonometric function — ગણિત ધોરણ 12 સાયન્સ — Question

Gujarat Boardગુજરાતી માધ્યમધોરણ 12 સાયન્સગણિત2. inverse trigonometric function1 Mark
MCQ
$\tan \left[ {{{\sin }^{ - 1}}\left( {\frac{3}{5}} \right) + {{\cos }^{ - 1}}\left( {\frac{3}{{\sqrt {13} }}} \right)} \right]$ =. . ..
  • A
    $\frac{6}{{17}}$
  • B
    $\frac{6}{{\sqrt {13} }}$
  • C
    $\frac{{\sqrt {13} }}{5}$
  • ✓
    $\frac{{17}}{6}$
✓

Answer

Correct option: D.
$\frac{{17}}{6}$
d
(d)$\tan \left[ {{{\sin }^{ - 1}}\left( {\frac{3}{5}} \right) + {{\cos }^{ - 1}}\left( {\frac{3}{{\sqrt {13} }}} \right)} \right]$
= $\tan \left( {{{\tan }^{ - 1}}\frac{3}{4} + {{\tan }^{ - 1}}\frac{2}{3}} \right)$ = $\tan \left( {{{\tan }^{ - 1}}\,\frac{{\frac{3}{4} + \frac{2}{3}}}{{1 - \frac{3}{4}.\frac{2}{3}}}} \right)$
= $\tan \left[ {{{\tan }^{ - 1}}\frac{{17}}{{12}} \times \frac{{12}}{6}} \right]$ = $\frac{{17}}{6}$.

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